Strong convergence theorem for Vilenkin--Fejer means

Abstract

Abstract. As main result we prove strong convergence theorems of Vilenkin-Fejér means when 0 < p ≤ 1/2.2010 Mathematics Subject Classification. 42C10.

On the convergence of Fejér means of Walsh-Fourier series in the space H p

“…Weisz [16] considered the norm convergence of Fejér means of Walsh-Fourier series and proved that (1) σ k F Hp ≤ c p F Hp , (F ∈ H p , p > 1/2) .…”

Strong convergence of two‐dimensional Vilenkin‐Fourier series

“…where v (n) and v * (n) are defined by (3) and λ := sup n∈N m n , according to (4) and (19) we have that (20) S n,n f (x, y)…”

On the Nörlund means of Vilenkin-Fourier series

“…In [5] it was proved that (2) holds, though Fejér means is not of type (H p , L p ) , for 0 < p ≤ 1/2. This result for (C, α) (0 < α < 1) means when p = 1/ (1 + α) was generalized in [4].…”